Kathryn Hess Bellwald

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Methods of topological data analysis have been successfully applied in a wide range of fields to provide useful summaries of the structure of complex data sets in terms of topological descriptors, such as persistence diagrams. While there are many powerful ...

Shadows for bicategories, defined by Ponto, provide a useful framework that generalizes classical and topological Hochschild homology. In this paper, we define Hochschild-type invariants for monoids in a symmetric monoidal, simplicial model category V, as ...

Let M be a monoidal category endowed with a distinguished class of weak equivalences and with appropriately compatible classifying bundles for monoids and comonoids. We define and study homotopy-invariant notions of normality for maps of monoids and of con ...

Worldwide, breast cancer incidence has been increasing for decades. Exposure to reproductive hormones, as occurs with recurrent menstrual cycles, affects breast cancer risk, and can promote disease progression. Exogenous hormones and endocrine disruptors h ...

Early intervention in psychosis is crucial to improving patient response to treatment and the functional deficits that critically affect their long-term quality of life. Stratification tools are needed to personalize functional deficit prevention strategie ...

Let K be a comonad on a model category M. We provide conditions under which the associated category of K-coalgebras admits a model category structure such that the forgetful functor to M creates both cofibrations and weak equivalences. We provide concrete ...

Working in the context of symmetric spectra, we describe and study a homotopy completion tower for algebras and left modules over operads in the category of modules over a commutative ring spectrum (eg structured ring spectra). We prove a strong convergenc ...

We apply the Acyclicity Theorem of Hess, Kedziorek, Riehl, and Shipley (recently corrected by Garner, Kedziorek, and Riehl) to establishing the existence of model category structure on categories of coalgebras over comonads arising from simplicial adjuncti ...

The lack of a formal link between neural network structure and its emergent function has hampered our understanding of how the brain processes information. We have now come closer to describing such a link by taking the direction of synaptic transmission i ...

A common technique for producing a new model category structure is to lift the fibrations and weak equivalences of an existing model structure along a right adjoint. Formally dual but technically much harder is to lift the cofibrations and weak equivalence ...

In this paper we consider two aspects of the inverse problem of how to construct merge trees realizing a given barcode. Much of our investigation exploits a recently discovered connection between the symmetric group and barcodes in general position, based on the simple observation that death order is a permutation of birth order. We show how to lift this combinatorial characterization of barcodes to an analogous combinatorialization of merge trees. As result of this study, we provide the first clear combina

The function of the neocortex is fundamentally determined by its repeating microcircuit motif, but also by its rich, hierarchical, interregional structure with a highly specific laminar architecture. The last decade has seen the emergence of extensive new ...

Persistent Homology (PH) has been successfully used to train networks to detect curvilinear structures and to improve the topological quality of their results. However, existing methods are very global and ignore the location of topological features. In th ...

In an application of the notion of twisting structures introduced by Hess and Lack, we define twisted composition products of symmetric sequences of chain complexes that are degreewise projective and finitely generated. Let Q be a cooperad and let BP be the bar construction on the operad P. To each morphism of cooperads g from Q to BP is associated a P-co-ring, K(g), which generalizes the two-sided Koszul and bar constructions. When the co-unit from K(g) to P is a quasi-isomorphism, we show that the Kleisli

Astrocytes connect the vasculature to neurons mediating the supply of nutrients and biochemicals. They are involved in a growing number of physiological and pathophysiological processes that result from biophysical, physiological, and molecular interaction ...

A consensus on the number of morphologically different types of pyramidal cells (PCs) in the neocortex has not yet been reached, despite over a century of anatomical studies, due to the lack of agreement on the subjective classifications of neuron types, w ...

One of the paramount challenges in neuroscience is to understand the dynamics of individual neurons and how they give rise to network dynamics when interconnected. Historically, researchers have resorted to graph theory, statistics, and statistical mechani ...

The organizational principles that distinguish the human brain from other species have been a long-standing enigma in neuroscience. Focusing on the uniquely evolved human cortical layers 2 and 3, we computationally reconstruct the cortical architecture for ...

How can we explain consciousness? This question has become a vibrant topic of neuroscience research in recent decades. A large body of empirical results has been accumulated, and many theories have been proposed. Certain theories suggest that consciousness ...

We introduce giotto-tda, a Python library that integrates high-performance topological data analysis with machine learning via a scikit-learn {compatible API and state-of-the-art C++ implementations. The library's ability to handle various types of data is ...

Kathryn Hess Bellwald

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From Trees to Barcodes and Back Again: Theoretical and Statistical Perspectives

A Shadow Perspective on Equivariant Hochschild Homologies

Normal and conormal maps in homotopy theory

Progesterone and Overlooked Endocrine Pathways in Breast Cancer Pathogenesis

Topology predicts long-term functional outcome in early psychosis

The homotopy theory of coalgebras over a comonad

Homotopy completion and topological Quillen homology of structured ring spectra

The Homotopy Theory Of Coalgebras Over Simplicial Comonads

Cliques of Neurons Bound into Cavities Provide a Missing Link between Structure and Function

A necessary and sufficient condition for induced model structures

From trees to barcodes and back again II: Combinatorial and probabilistic aspects of a topological inverse problem

Modeling and Simulation of Neocortical Micro- and Mesocircuitry. Part I: Anatomy

Persistent Homology with Improved Locality Information for more Effective Delineation

Twisting structures and strongly homotopy morphisms

Digital Reconstruction of the Neuro-Glia-Vascular Architecture

Objective Morphological Classification of Neocortical Pyramidal Cells

Topological exploration of artificial neuronal network dynamics

Of mice and men: Dendritic architecture differentiates human from mouse neuronal networks

The unfolding argument: Why IIT and other causal structure theories cannot explain consciousness

giotto-tda: A Topological Data Analysis Toolkit for Machine Learning and Data Exploration